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The geometrical structure of Y3Al5O12 (YAG) crystal was optimized by using first-principles calculation scheme, i.e. generalized gradient approximation (GGA) with the PW91 exchange correlation potential and “on the fly” pseudo-potential (OTFPP). The obtained lattice parameters are in good accordance with experimental results reported in the literature. This confirms the validity of the present GGA-OTFPP scheme. The total energy, populations, and contour maps of total charge density of YAG system were calculated with the same scheme. The derived formation energy (-2.396eV) indicate the good stability of the structure. The obtained Mulliken charge populations of atoms, overlap populations, as well as contour maps of total charge density congruously show that YAG crystal is a mixed bond material with stronger ion bond and weaker covalence bond.

The equilibrium structures of orthorhombic LaCrO3(O-LaCrO3) and rhombohedral LaCrO3(R-LaCrO3) crystals were investigated by using the plane-wave self consistent field (PWSCF) method based on density functional theory (DFT). The optimized lattice parameters for both phases are in accordance with experimental results reported in literature, confirming the reliability of LSDA+U scheme used in the calculations. We have quantificationally investigated the binding energies and electronic properties of these two types of LaCrO3crystals. The negative total energy and binding energies indicate the ground state property and the good structrual stability of O-LaCrO3crystal, which is important for the preparation of nano materials, the synthesis of ceramic materials made of doped O-LaCrO3crytals, as well as their applications in high technology fields, and predict the metastable property of R-LaCrO3crystal. Furthermore, the band structures show that O-LaCrO3is a direct semiconductor with wide energy gap, while R-LaCrO3is an indirect semiconductor with narrow energy gap. The interaction between Cr and O atoms in O-LaCrO3crystal possesses the character of covalent bonding.